Solve for $x$ and $y$ using substitution. ${-5x+4y = 0}$ ${y = -x+9}$
Solution: Since $y$ has already been solved for, substitute $-x+9$ for $y$ in the first equation. ${-5x + 4}{(-x+9)}{= 0}$ Simplify and solve for $x$ $-5x-4x + 36 = 0$ $-9x+36 = 0$ $-9x+36{-36} = 0{-36}$ $-9x = -36$ $\dfrac{-9x}{{-9}} = \dfrac{-36}{{-9}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {y = -x+9}\thinspace$ to find $y$ ${y = -}{(4)}{ + 9}$ $y = -4 + 9$ $y = 5$ You can also plug ${x = 4}$ into $\thinspace {-5x+4y = 0}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ + 4y = 0}$ ${y = 5}$